_ R + 0,25 ■ d, • sin Ф
'ap ~ R + 0,5 -dm ■ sin
ivy= - cos Ф,і„ = - sin Ф
imx= 1 for outside, imx= for inside
Table C.10 — Stress intensification factors for bends
|
|
Out-of-plane moment, ДЛ4У |
In-plane moment, AMZ |
|
Outside |
^ау ~ ^amy + hby hy ~ Ifby |
iaz ~ iamz + Itbz Itz ~ Ifmz "*■ Itbz |
|
Inside |
lay ~ lamy~ У Itby Ify Itby |
Iaz ~ Iamz " itbz Itz ~ hmz ~ Itbz |
For out-of-plane moments, дМу:
, (1,5 • x2 -18,75) • cos ЗФ + 11,25 • cos 5Ф
lamy= cos Ф + 2-
*4
. 9 ■ x, • sin 2d> + 225 sin 4Ф
4 =
*4
For in-plane moments, Mz:
. . (1,5 x, -18,75) sin ЗФ + 11,25 sin 5Ф
'aznz = Sin Ф + 2-
*4
, 9 • x, ■ cos 2Ф + 225 cos 4Ф
!tbz= A 2-
Л4
_ cdm, . , (0,5 ■ x2 - 6,25) • cos ЗФ + 2,25 cos 5Ф.
/tmz = -0,5 — cos ■ (cos Ф + — 2- —- )
R x4
where
x1= 5 +6 A2+ 24 у
x2 — 17 + 600A2+ 480 у/
x3 = хлх2- 6,25
x4= (1-A)(x3-4.5x2)
d2m -Vl-v2
and
P f?2E d-t.
C.7.6 Tees
In tees the maximum membrane stresses from internal over-pressure will occur in point A (top point) in Figure C.9, whereas the impact from internal forces is limited at this point.
Maximum stresses from internal forces in run pipe and the branch (including normal force from pressure) usually occur in the vicinity of point В (saddle point) in Figure C.9, whereas internal over-pressure is of minor importance here. For large in-plane moments in the branch maximum stresses can occur at point A.
However, the simplified methodology described below presupposes that for fatigue analysis all stresses are referred to point B.
In most cases it is therefore sufficient to assess limit state A1 in point A and limit state B1 in point B.
Consequently the strength verification shall be carried out separately for both points. For pipelines with large normal forces, point В will normally be decisive for the dimensions.
Stress contributions are calculated from the formula expressions given in C.7.3, using the values for iap, ia1- ia5, d, t, W, and A valid for run pipe and branch, respectively.
Figure C.9 — Symbols for tees
Stress intensification factors for tees in point A:
Іа1 ~ Іа2 ~ ІаЗ ~ >a4 ~ >a5~0
. _ 1
>aP~ ( ri
1-0,3084 In -ySg—
к • fb ,
Table C.11 — Stress intensification factors for membrane stresses in point В of tees (all types)
|
Membrane stresses <ym |
Ia1 <Ta(&NX) |
>a2 <та(ДМУ, ДМ?) |
ІаЗ т (ДМ,) |
!q4 Т (AVy>AVZ) |
|
Run pipe |
Ггк 2 |
rrk. |
2rrкг |
Гг |
|
Branch pipe |
rbк |
rbк |
rbк |
rbк |
Table C.12 — Stress intensification factors for resulting stresses in point В
|
Resulting stresses crres |
Іа1 &a (ДМ*) |
Іа2 aa(ДМу, ДМг) |
ІаЗ т (ДМ,) |
^a4 Т (ДУу, |
|
Fabricated tee Run pipe |
1,2 k2 |
ki |
2-кі |
кг |
|
Branch pipe (note 3) |
к |
к |
к |
к |
|
Weld-in tee (note 1) Run pipe |
0,7 k2 |
0,6 кг |
1,2 |
0,6 |
|
Branch pipe (note 3) |
0,4 к |
0,4 k |
0,4 к |
0,4 к |
|
Extruded tee (note 2) Run pipe |
0,8 k2 |
0,7 ki |
1,4 |
0,7 |
|
Branch pipe (note 3) |
0,7 к |
0,7 к |
0,7 к |
0,7 к |
Іа5 = lap = 0 ІП point B.
. _ ( 1 V Ґ 1V ( cL }
*,=0,523- — ■ - -dbm +2,5- 1--^
UJ I drmJ
z z Л z Л
. ( і V (і V z з ( d . л V
k2=0,65- — I .(dbm)i+ 2,5- 1--^
rm J lr ) V Vrm ' ‘r 7
к = 0,567
Reduction factors for membrane stresses.
5
